Precision Plasmonics with Monomers and Dimers of Spherical Gold

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Feature Article

Precision Plasmonics with Monomers and Dimers of Spherical Gold Nanoparticles: Non-Equilibrium Dynamics at the Time and Space Limit Ludmilla Schumacher, Jesil Jose, David Janoschka, Pascal Dreher, Timothy J. Davis, Manuel Ligges, Renkai Li, Mianzhen Mo, Suji Park, Xiaozhe Shen, Stephen Weathersby, Jie Yang, Xijie Wang, Frank J. Meyer zu Heringdorf, Klaus Sokolowski-Tinten, and Sebastian Schlücker J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01007 • Publication Date (Web): 17 Apr 2019 Downloaded from http://pubs.acs.org on April 17, 2019

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The Journal of Physical Chemistry

Precision Plasmonics with Monomers and Dimers of Spherical Gold Nanoparticles: Non-Equilibrium Dynamics at the Time and Space Limit †

L. Schumacher,

Li,

¶

¶

†

J. Jose,

¶

M. Mo,

S. Park,

¶

X. Shen,

zu Heringdorf,

†Department

D. Janoschka,

∗,‡

‡

P. Dreher,

¶

S. Weathersby,

T.J. Davis,

J. Yang,

∗,‡

K. Sokolowski-Tinten,

‡

¶

‡,§

‡

M. Ligges,

X. Wang,

¶

R.

F. Meyer

∗,†

and S. Schlücker

of Chemistry and Center of Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, 45141 Essen, Germany

‡Department

of Physics and Center of Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, 47057 Duisburg, Germany

¶SLAC §present

National Accelerator Laboratory, Menlo Park, California 94025, USA

address: School of Physics, University of Melbourne, Parkville 3010, Australia

E-mail: [email protected]; [email protected]; [email protected]

Abstract Monomers and dimers of spherical gold nanoparticles (NPs) exhibit highly uniform plasmonic properties at the single-particle level due to their high structural homogeneity (precision plasmonics). Recent investigations in precision plasmonics have largely focused on static properties using conventional techniques such as transmission electron microscopy and optical dark-eld microscopy. In this feature article 1

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we rst highlight the application of femtosecond time-resolved electron diraction for monitoring the non-equilibrium dynamics of spherical gold NPs after ultrafast optical excitation. The analysis of the transient diraction patterns allows us to obtain directly quantitative information on the incoherent excitation of the lattice, i.e. heating upon electron-lattice equilibration, as well as on the development of strain due to lattice expansion on picosecond time-scales. The controlled assembly of two spherical gold NPs into a dimer with a few nm gap leads to unique optical properties. Specically, extremely high electric elds (hot spot) in the gap are generated upon resonant optical excitation. Conventional optical microscopy cannot spatially resolve this unique hot spot due to the optical diraction limit. We therefore employed nonlinear photo-emission electron microscopy (PEEM) for visualizing hot spots in single dimers of spherical gold NPs. A quantitative comparison of dierent single dimers conrms the homogeneity of the hot spots on the single-particle level. Overall, these initial results are highly encouraging as they pave the way to investigate the non-equilibrium dynamics in highly uniform plasmonic nanostructures at the time and space limit.

Introduction Noble metal nanoparticles (NPs) support localized surface plasmon resonances (LSPR) upon optical excitation: when the incident optical frequency is resonant with the plasma frequency then the oscillating electric eld of the light wave drives the coherent oscillation of the free electron gas in the metal (see Fig. 1). After the excitation of a LSPR, also called particle plasmon in order to distinguish it from propagating plasmons in an extended lm, there are two distinct decay channels: a radiative pathway (scattering) and a nonradiative pathway (absorption). 1 In the radiative pathway (Fig. 1 top) the metal NP acts as a nanoantenna which emits radiation as a Hertzian dipole with nanoscale dimensions. Since the frequency of the emitted photons is the same as the one of the incident photons elastic scattering takes place which can be measured from single particles, for example, in a dark-eld microscopic conguration.

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Figure 1: Photoexcitation and subsequent decay processes in a plasmonic nanoparticle following illumination with laser pulse. The incident electric eld induces oscillation of free electron gas in the nanoparticles called plasmon resonances. These plasmons are damped radiatively by the re-emission of photons (top)and non radiatively via the hot carrier generation and subsequent lattice heating due to carrier-phonon coupling (bottom) Telectron , Tlattice and Troom represents the temperature corresponding to the electron lattice and room respectively. In the non-radiative pathway (Fig.1 bottom), the metal NP essentially acts as an absorbing medium in which charge separation occurs and hot charge carriers (hot electrons and hot holes) are generated. After electron-electron scattering, occurring on a femtosecond time scale, the energy initially stored in the electronic system, is dissipated to the lattice on ps time-scales via electron-phonon coupling processes 2 . The plasma frequency or plasmon wavelength for which this LSPR occurs depends on parameters such as metal/material, size, shape and the surrounding medium. The latter has been extensively exploited for LSPR sensing. 3 Also the dierent decay channels of a plasmon can be exploited in various areas of physical chemistry, medicine and material science. Surface-enhanced Raman scattering (SERS) 4 of molecules adsorbed on noble metal nanoparticles is a prominent representative of a whole class of surface-enhanced molecular spectroscopic techniques (SE Raman/IR/uorescence). Essentially, the locally enhanced electric eld due to LSPR excitation leads to very large induced dipoles creating intense Raman scattering. In this 3



sense the metal nanoparticle acts as an optical enhancer for this type of plasmon-assisted scattering from molecules. In addition to this "passive" way of the radiative channel (scattering) employed in optical spectroscopy, the non-radiative channel (absorption) has attracted more and more attention in recent years. The localized generation and extraction of hot carriers emerges as an attractive route for applications in photovoltaics, -chemistry and -catalysis 1,59 . However, the carrier life time is limited by electron-phonon coupling processes and the energy transfer to the phonon system leads to rapid heating of the lattice. Therefore, NPs are also used as nanoscale sources of thermal and mechanical energy (see review by Baou et al. 10 and references therein). The strength of electron-phonon coupling depends on the specic material, but is also inuenced by the sample morphology. In particular, at the nano-scale size and shape as well as surface and interface eects can play an important role 11,12 . The majority of experimental work addressing electron-phonon coupling in NPs makes use of time-resolved optical techniques. e.g. femtosecond transient absorption (see review by Hartland et al. 13 and references therein). More recently also ultrafast X-ray or electron diraction/scattering has been applied to directly monitor various aspects of the structural response of nano-structured materials upon optical excitation 1431 . Here we extend our previous time-resolved diraction studies on the electron-lattice relaxation in nano-scale Au 26,29 to the case of highly spherical NPs (AuNS, section 2). This allows us to obtain directly quantitative information on the incoherent excitation of the lattice (i.e. heating) upon electron-lattice equilibration, as well as on the development of strain due to lattice expansion. A single noble metal nanoparticle may be viewed as the equivalent of a single atom in molecular chemistry. Similar to molecular chemistry, where molecules can be considered as an assembly of atoms sharing electrons by bonding molecules orbitals, assemblies of more than one metal particle exhibit new physical properties. A dimer of two metal nanoparticles is the simplest case for which plasmonic coupling, the analogue of the LCAO concept in quantum chemistry, occurs. The arrow in Fig.2 indicates the generated dipole moment, i.e., charge separation, upon LSPR excitation.

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Figure 2: (a)The plasmon hybridization diagram for a dimer of spherical gold nanoparticles. Hybridization results in the formation of bonding and antibonding plasmon modes which are lower and higher in energy, respectively with reference to a monomer plasmon mode, arrows represent the direction of induced dipole. Dark plasmon modes are modes with zero eective induced dipole moment which makes them invisible in optical spectroscopy. The enhancement of electric eld in the junction between the dimer is evident from the neareld diagram. (b)The blue curve represents the LSPR coupling mode of the monomer and the redshifted curve represents the longitudinal bonding dipolar mode of the dimer. 32,33 The coupling of the dipoles excited on the two spheres in a dimer can occur in the direction of the dimer axis (σ -type orbital in quantum chemistry terms) or perpendicular to it (π -type orbital in quantum chemistry terms). Overall, four new plasmon modes arise: two bonding modes with energies lower and two anti-bonding modes with energies higher than the energy required for the LSPR excitation in a single sphere. 32,33 In other words, a dimer of two noble metal nanoparticles may be considered at the colloidal equivalent of a homonuclear diatomic molecule such as molecular hydrogen (H2 ), nitrogen (N2 ), oxygen (O2 ) or a halogen (X2 ). Only the two plasmon modes associated with a dipole moment are observable in optical spectroscopy: the longitudinal bonding dipolar 5



plasmon (LBDP) mode with the lowest energy (highest wavelength) and the transversal antibonding dipolar plasmon mode with the highest energy (lowest wavelength). Theory employs idealized structures such as perfect spheres. Experimentalists have been lacking long behind in preparing such perfect noble metal nanoparticles. Only since a few years colloid chemists are able to synthesize highly round gold nanoparticles by etching (oxidizing) the more reactive atoms at higher-order facets, thereby paving the way to precision plasmonics, i.e., high reproducibility at the single-particle level. 34 These highly spherical gold nanoparticles or gold nanospheres (AuNS) can then be assembled into highly dened ideal dimers with gap control at the Angstrom level by using molecular linkers (section 3). Their single-particle dark-eld scattering spectra exhibit an unprecedented homogeneity and the LDBP mode occurs at highly uniform positions with a very narrow standard deviation. This is in stark contrast to the situation in non-ideal dimers comprising the same gap distance (same linker molecule) but faceted building blocks: here, the LBDP position varies across many tens of nm due to the many dierent possibilities for the conguration of the crystal facets in the gap (dierent gap morphologies). A unique feature in dimers of noble metal NPs with very short gaps (few nm) is the occurrence of a hot spot upon resonant excitation, i.e., a highly conned (few nm3 ) volume with extremely high local electric elds (Fig.2). This hot spot can be exploited for highly sensitive vibrational spectroscopy of molecules located in the gap (single-molecule SERS). 35,36 The very high electric elds can also be exploited for driving chemical reactions 37 or for eciently generation hot carriers REF such as hot electrons which can be transferred to adjacent semi-conductors or molecular adsorbates (electron transfer reaction). Techniques of conventional optical microscopy cannot fully spatially resolve the hot spot due to the optical diraction limit. Resolving the hot spot in a dimer with nanometer resolution can, however, be achieved with electron microscopy. In this case the plasmon-induced non-equilibrium dynamics is probed by an optical probe pulse which in a multi-photon transitions leads the ejection of detectable electrons. Specically, we demonstrate the use of nonlinear photo-emission electron microscopy (PEEM) for localizing hot spots in dimers of AuNS with high spatial resolution after ultrafast optical excitation. Furthermore, we demonstrate that in addi-

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tion to the highly uniform elastic scattering spectra also the hot spot in two dierent ideal dimers is highly uniform. Overall, these initial results are highly encouraging as the demonstrate the feasibility of precision plasmonics of single ideal colloidal particles at the limits of time (femtosecond electron diraction) and space (PEEM) after ultrafast optical excitation.

Monomeric Spherical Gold Nanoparticles In this section we discuss experiments, which investigate the nal step of the non-radiative relaxation channel in laser-irradiated NPs, namely the transfer of energy from the hot electronic system (after decay of plasmonic excitations), to the lattice. We use deposited lms of mono-disperse highly spherical AuNS as samples, which removes inhomogeneous broadening eects in the corresponding optical spectrum of the particle lm as well as in its structural response. The synthesis of the AuNS is done by a seed-mediated growth method, where cetyltrimethylammonium bromide (CTAB) is employed as the stabilizing agent. In the last step of the synthesis the obtained icosahedral nanoparticles are etched by mild oxidation with tetra chloroauric(III)acid (HAuCl4). 38 The resulting particle are round since the gold atoms with high-order facets have been removed. The size of the AuNS can be controlled by the ratio of the concentration of the seed particles to the concentration of tetrachloroauric(III)acid and the reducing agent. 39 Fig.3 (left) shows transmission electron microscopy (TEM) images of ca. 50 and ca. 80 nm large AuNS, demonstrating that the particles exhibit a high degree of monodispersity and roundness. The dynamic light scattering (DLS) data in Fig.3 (right) (hydrodynamic radius of ca. 31 nm and ca. 42 nm, respectively) and the corresponding UV/vis extinction spectra in Figure 3 (middle) (plasmon peak centered at ca. 528 nm and 542 nm) both indicate a narrow size distribution for the AuNS dispersed in water. Due to the use of CTAB as the detergent with a positively charged quaternary ammonium group the AuNS show a positive zeta potential (11.6 mV and 5.6 mV).

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Figure 3: Characterization of ideal gold spheres of varying size using dierent techniques: Transmission electron microscopy (TEM) reveals that both 50 nm and 80 nm spheres are highly uniform in size and structure. (left) Extinction spectra of monomer spheres showing an increased scattering for the bigger 80 nm particles as expected. (middle) Zeta potential measurements and dynamic light scattering (DLS)showing that the particles are positively charged due to the presence of CTAB capping agent and the hydrodynamic radius, respectively. (Right) The structural response of such AuNS has been investigated by ultrafast time-resolved electron diraction. For this purpose 50 nm AuNS have been deposited onto a 20 nm thick Si3 N4 -membrane in a Si wafer frame with a coverage of approx. 0.05. Experiments were carried out at the MeV Ultrafast Electron Diraction (UED) facility at SLAC National Accelerator Laboratory 40 . UED@SLAC employs a fs laser-driven RF photo gun and provides ultrashort electron pulses at relativistic energies. Here we used pulses of a few times 105 electrons per pulse, 200 fs FWHM bunch duration, and 3.7 MeV kinetic energy at a repetition rate of 120 Hz. Using a normal incidence transmission geometry (see schematic in Fig. 4a) the diraction pattern were recorded by a single electron sensitive area detector, which was placed 3.5 m away from the sample providing a momentum resolution of about 0.14 Å−1 . For the time-resolved experiments the frequency doubled output (wavelength 400 nm,

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(a)

diffraction pattern

Difference [a.u.] Scatt. int. [a.u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


fs laser pump

fs MeV e- probe

Au NP on Si3N4

1

111

(b) 220

0.5

200

0 0.02

311

331 440 420 422 531 511 622 400

(c)

0 -0.02

(4 ± 1) ps (40 ± 5) ps

2

4

6

q [Å-1 ]

8

10

Figure 4: (a): Schematic of the experimental geometry. Spherical Au NPs of (50 ± 2.5) nm diameter deposited on 20 nm Si3 N4 membranes are irradiated with 60 fs, 400 nm laser pulses (near normal incidence). Their structural response is probed by diraction of 200 fs, 3.7 MeV kinetic energy electron pulses in normal incidence transmission geometry. (b): Scattering intensity I(q) of the unpumped sample as a function of momentum transfer. (d): Dierence scattering pattern for delay times ∆t = 4 ps (red) and ∆t = 40 ps (black) after laser excitation (F = 6.3 mJ/cm2 ). pulse duration 60 fs FWHM) of the Ti:sapphire laser that drives the photogun is used for sample excitation in a quasi-collinear geometry (angle of incidence 3 deg.). Both, the optical pump pulse as well as the electron probe pulse (by a solenoid), were focused onto the sample to spot sizes of about 400 µm and 200 µm (FWHM), respectively. Fig. 4b shows the background corrected scattering signal I(q) of the non-excited sample as a function of momentum transfer q ≈ 2π/λ · θ (λ = 0.003 Å: De Broglie wavelength,

θ: Scattering angle) obtained by azimuthal integration (along lines of constant q ) of the diraction pattern recorded by the area detector. All observed diraction peaks correspond to the known reections of Au (labelled by their corresponding Miller indices). Upon optical excitation the diraction intensity changes as can be seen in Fig. 4c showing transient dierence scattering pattern ∆I (q, ∆t) = I (q, ∆t) − I0 (q) (I0 (q): unpumped) for time delays ∆t of 4 ps (red) and 40 ps (black-dashed), respectively, at an excitation uence F = 6.3 mJ/cm2 . A time-dependent decrease of the Bragg-peak intensities as well as an increase of the diuse background between the peaks can be recognized. As will be discussed in detail later, both features can be (mainly) attributed 9



to the increase of the r.m.s. atomic displacement in the Au NPs after optical excitation. For a quantitative analysis the integrated signal of those Bragg-peaks, which are either suciently strong or well separated from other peaks, has been determined through tting with a Gaussian function superimposed on a (linear) background for each pump-probe time delay ∆t. As a result Fig. 5a shows the integrated diraction eciency for several Bragg peaks for the same pump uence of F = 6.3 mJ/cm2 as in Fig. 4c. The diraction signal has been normalized to the value measured at negative delay times, i.e. before sample excitation. As violet data points Fig. 5a also depicts the time dependence of the diuse scattering signal measured between the (200)- and (220)-reection from 3.5 Å−1

diffuse 111/200

6.3 mJ/cm 2

0.02

0.3

0.015

220

0.8

0.2

0.6

0

(b)

422

10

20

Delay time [ps]

0.01 400

3 mJ/cm 2 3 mJ/cm 2

0.7

(a)

500

0

20

40

60

q2 [Å2 ]

80

0.1 0

0.005

(c)

0 0

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300

6.3 mJ/cm 2

4

2 3 mJ/cm

2

-3

331/420

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6.3 mJ/cm 2

(d) 0

20

40

Strain [x 10 ]

0.9

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∆u2 [Å2 ]

1

Temperature [K]

Scattering intensity [norm.]

to 3.9 Å−1 .

-ln(I∞/I0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0

60

Delay time [ps]

Figure 5: (a): Normalized integrated diraction eciency of various Bragg-peaks (hkl) as a function of pump-probe time delay; the violet data points show the diuse scattering signal measured at q = (3.7 ± 0.2) Å−1 . Pump uence F = 6.3 mJ/cm2 (b): Asymptotic logarithmic intensity change (averaged from 40 ps ≤ ∆t ≤ 60 ps) as a function of G2hkl (c): Change of the r.m.s. atomic displacement as a function of pump-probe time delay (right ordinate: Derived lattice temperature); the black solid and dashed curves represent results of calculations based on the two-temperature model for dierent electron-phonon coupling parameter (see Eq. (2)). (c): Strain as a function of pump-probe time delay; black curves represent a guide to the eye. In (a) to (c) blue and red data points represent experimental results for F = 3 mJ/cm2 and F = 6.3 mJ/cm2 , respectively. While the dierent Bragg-peaks exhibit an order-dependent decrease within a few ps, the diuse scattering intensity increases on similar time-scales. This can be attributed to the transient Debye-Waller eect. Within the Debye-Waller model the intensity decrease of Bragg-peaks Ihkl (∆t) is caused by the increase of the r.m.s. atomic displacement

∆hu2 i(∆t) and can be expressed as:

10


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Ihkl (∆t) =

0 Ihkl

− 13 G2hkl ∆hu2 i(∆t)

·e

Ihkl (∆t) ⇔ −ln 0 Ihkl

!

1 = G2hkl · ∆hu2 i(∆t) 3

(1)

0 Herein Ihkl denotes the scattering signal measured at negative time delays and Ghkl

the length of the reciprocal lattice vector corresponding to reection (hkl). While our experiment is only sensitive to atomic motion parallel to the surface of the Si3 N4 -membranes used as substrates due to the normal-incidence geometry and the very short de-Broglie wavelength (i.e. extremely at Ewald-sphere), we assume with Eq. 1 an isotropic response. This assumption is justied here, since Au is an isotropic material and the particles are deposited with random orientation, but can be violated for unisotropic materials and textured samples 22 . The logarithmic form of the Debye-Waller equation is particularly useful to verify whether the structural response is incoherent and can be described solely by the increase of the r.m.s. atomic displacement: Plotting the negative logarithm of the normalized intensity as a function of G2hkl should result in a linear dependence with a slope determined by ∆hu2 i. Fig. 5b shows these dependencies for the asymptotic intensity I∞ (signal averaged over the delay range 40 ps ≤ ∆t ≤ 60 ps) as a function of G2hkl for pump uences

F = 3 mJ/cm2 (blue) and F = 6.3 mJ/cm2 (red), respectively. The measured data follow indeed the linear behavior expected from the DW-model indicating that the lattice response is dominated by incoherent, statistical atomic motion. We veried that the Debye-Waller-model describes the experimental data for all delay times, and, therefore, the diraction data can be used to determine ∆hu2 i as a function of delay time as shown in Fig. 5c. In a subsequent step we used published data on the temperature dependence of the Debye-Waller-factor of Au 41,42 to convert the experimental ∆hu2 i (∆t) into the transient temperature rise ∆T (∆t). The result of this conversion is shown in Fig. 5c at the right ordinate, indicating that excitation at 3 mJ/cm2 and 6.3 mJ/cm2 leads to a maximum temperature rise of 135 K and 295 K, respectively. We would like to stress that this conversion into temperature should in principle be treated with some care for two reasons: (i) Considerable and material-specic changes 11



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of the phonon spectrum (e.g. phonon softening 4345 ) can occur by electronic excitation, which eectively leads to a temporally varying Debye-temperature of the material. Although phonon hardening has been predicted in the case of Au at very high electronic temperatures 46 we do not expect such eects to be important at the excitation level of our experiment. (ii) Even for simple metals like Au there is experimental 47,48 as well as theoretical 49 evidence that the phonon population generated through electronic relaxation is non-thermal for rather long time-scales (i.e. 10s of ps). Thus, the notion of a lattice temperature is strictly speaking not valid. Being aware of these limitations we nevertheless use the temperature concept to quantitatively analyze the energy ow in the system in the frame of the well-known twotemperature model 50 (TTM). The TTM assumes separate, but thermalized distributions for electrons and phonons, respectively, and describes the response of the material by heat diusion equations for the two sub-systems coupled through the electron-phonon coupling parameter g . Additionally, we assume a spatially homogeneous deposition of the optical energy into the electronic system since the ballistic range of excited electrons in Au of about 100 nm 51,52 is larger than the particle diameter. Due to the short pump pulse duration and the few ps time-scale of interest (as revealed by the experimental data), an instantaneous and homogegenous increase of the electronic temperature was chosen as starting condition instead of an explicit laser source term. This results in the following, only time-dependent equations:

−ce

∂TL ∂Te = cL = g (Te − TL ) ∂t ∂t

(2)

Herein ce and cL denote the electronic and lattice specic heat, respectively, and g the electron-phonon coupling parameter. Given the simplied nature of this description we use ce = 67.6 J/ (m3 K2 ) · Te and a constant lattice specic heat cL = 2.5 MJ/ (m3 K). The electron-phonon coupling parameter is assumed to be constant as well, but treated as free a parameter in the calculations. The solid and dashed black curves in Fig. 5c represent the results of such calculations. From a comparison with the experimental data we determine g = 1.8 × 1016 W/ (m3 K) (solid curve) with an error of ∆g = ±0.2 × 1016 W/ (m3 K) 12


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(dashed curves). Within the accuracy of the experiment this is in agreement with the value of g = 1.7 × 1016 W/ (m3 K) for bulk Au obtained from electron diraction experiments on free-standing as well as supported thin lm Au-samples 26,29 , but lower than the value we have measured for nano-porous Au 29 . In the latter case the observed 30% increase of the electron-phonon coupling strength has been attributed to the "spill-out" of conduction band electrons at the surface of the nanostructured material, which leads to a reduced screening of the core potential of atoms in the surface region and thus to stronger electron-ion interactions. This mechanism has been introduced by Arbouet et al. 11 to explain the results of time-resolved optical data on Au and Ag nano-particles, which provided evidence for a speed-up of the electronic relaxation with decreasing particle size. In particular, their data indicate that these eects become increasingly important for particle sizes below 15 nm. In line with these observations we determine for the 50 nm particles studied here an electron-phonon coupling parameter very close to the value of bulk Au. Beside the time-dependent reduction of the diraction intensity we also observed a shift of the peaks towards smaller diraction angles. While these shifts are relatively small (approx. 1 pixel on the area detector for the highest order reections at F = 6.3 mJ/cm2 ) they are strictly proportional to the length of the corresponding reciprocal lattice vector:

∆qhkl = η · Ghkl . Therefore, the proportionality constant η can be directly associated with strain due to expansion of the particle. As can be seen in the inset of Fig. 5c, the strain exhibits a similar time-dependence as the increase of the r.m.s. displacement with slight indications of a small oscillatory contribution (the black-dashed curves represent a guide to the eye) at the higher pump uence. Such oscillatory behavior is actually expected and has been observed in many studies, both for thin lms (e.g. 53,54 ) as well as for NPs 55,56 . For spherical particles it corresponds to radial acoustic "breathing" modes which are triggered by the impulsive laser-induced increase in stress/pressure 57,58 . The close correspondence between the temporal evolution of strain and r.m.s. atomic displacement as well as the small oscillation amplitude seem to indicate that the acoustic waves are strongly damped. However, the noise of the strain data prohibits a further

13



analysis/interpretation of the oscillatory contribution and we will, therefore, focus on the absolute magnitude of the overall strain. For late time delays we determine a strain of (1.9 ± 0.1) × 10−3 and (3.9 ± 0.2) × 10−3 for pump uences of 3 mJ/cm2 and 6.3 mJ/cm2 , respectively. Taking into account that such small particles can expand freely in all dimensions on ps time scales and using the known linear thermal expansion (temperature dependent) of Au 59 an asymptotic temperature increase of (135 ± 7) K and (275 ± 15) K is obtained for the two uences. This is consistent with the temperature directly derived from the ∆hu2 i-data providing some justication to use a temperature approach for the quantitative analysis of our data. In summary, time-resolved diraction with femtosecond, relativistic electron pulses has been used to investigate the structural response of spherical Au NP upon ultrafast laser excitation. From our data we directly determine the transient increase of the r.m.s. atomic displacement and thus the temporal evolution of the lattice temperature during electron-lattice equilibration. Calculations based on the two-temperature-model using an electron-phonon coupling parameter g = (1.8 ± 0.2) × 1016 W/ (m3 K) are in good agreement with the experiments. Furthermore, we observe the evolution of strain within a few ps, which can be consistently interpreted as thermal expansion of the laser-heated NP. Our results demonstrate the possibilities of time-resolved diraction for the study of plasmonic nanoparticles.

Ideal Dimers of Spherical Gold Nanoparticles As discussed in the introduction(Fig 2), dimers exhibit new plasmon modes due to plasmon hybridization and hot spot after resonant excitation of the LBDP mode along the dimer axis. The optical properties of dimers strongly depend on both the shape of the building blocks and their distance. Precision plamonics on single dimers requires of spherical building blocks assembled at small gap distances with angstrom-resolution. Ideal dimers of AuNS can be synthesized by a solid phase-supported approach. The rst AuNS is deposited on a glass slide via electrostatic binding. 60 The CTAB bilayer of

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the adsorbed AuNS is destabilized by a combination of polar organic solvents (ethanol, acetonitrile) and sodium bromide. 61,62 The 2nd AuNS is conjugated to the 1st AuNS by a linker molecule (alkyl dithiol). 63 Figure 6 left shows scanning electron microscopy (SEM) image of ideal 50nm AuNS dimers and top right transmission electron microscopy (TEM) images of ideal dimers of AuNS for dierent monomer size, 50 nm and 80 nm). The high yield of the synthesis (close to 90%) and the high uniformity of the ideal dimers is evident. The 50nm AuNS dimers as well as the 80 nm AuNS dimers are linked with 1,8-octanedithiol (C8 ) molecule. Due to the high degree of geometrical uniformity also the corresponding single-particle dark-eld scattering spectra for both sizes )are highly uniform as shown in Figure 6 down right. The peak at ca. 721 nm in the case of the 50nm AuNS dimers is assigned to the longitudinal dipolar bonding plasmon coupling mode. An increase in size of the monomeric building block leads to a redshift in the longitudinal bonding dipolar mode (LDBP) band. As shown here the assembly strategy works equally well also for larger AuNS (e.g., 80 nm instead of 50 nm) and also alkyl dithiol linkers with a dierent chain length (e.g., 1,10-decanedithiol (C10 ) instead of C8 ). 34

None of the above mentioned techniques provides insights into the local electric eld enhancement in the gap of the AuNS dimers. The direct visualization of these ultra-low volume cavities were always o limits due to the optical diraction limit. This fundamental problem can be overcome by using the non-linear photoelectron emission spectroscopy (PEEM) where we use electrons as probe. Electrons with their sub nanometer wavelength can provide us the spatial resolution that is required to probe the gap distance of the order of few angstrom.

The ideal dimer system consisting of two 80 nm dimers separated by a gap distance of approximately 1.5 nm is used in the PEEM studies. The PEEM experiments were performed in Ultrahigh Vacuum (UHV) using a spectroscopic photoemission low energy electron microscope (SPE-LEEM) made by Elmitec GmbH. The microscope was primarily used in three dierent operation modes.

15



Figure 6: Characterization of ideal dimers by common techniques: SEM image of the ideal 50nm AuNS dimers (left) Comparison of TEM images of dimers with same gap distance (1.3 nm) and dierent monomer size (50 nm and 80 nm) and their corresponding LSPR scattering spectra. (right) As evident from the image, an increase in size of the constituent monomers leads to an ecient coupling of the plasmons in the junction leading to a redshift in the LBDP (bonding mode) band. The unprecedented uniformity in the structure is evident from the near uniform position of LBDP bands for dierent dimers and their narrow standard deviations. First, the particles were located using threshold PEEM, i.e., the surface was illuminated with ultraviolet light from a Hg discharge lamp, and the emitted electrons were used to form an image in the microscope. Examples for PEEM images of dimers and quadrumers are given in panels (a) and (b) of Fig. 7, respectively. The electron optical resolution of the SPE-LEEM is about 11 nm, and the PEEM images of the dimers and the quadrumers show the typical blurring that is common in threshold PEEM. Still, the individual local intensity maxima correspond to the number of particles in the oligomer. If more detailed information about the arrangement of the particles is desired, the second method used in our study comes into play. Using an electron beam of an energy where the electrons are reected at the surface potential (mirror electron microscopy (MEM) 64,65 ) enhances the contrast at the edges of the particles. Panels (c) and (d) of Fig. 7 show MEM images of the same oligomers that were imaged with threshold PEEM before. In the MEM images the perimeter of the particles appears bright, while the particle themselves are imaged dark. From the transition of black to white regions across the particle 16


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we can estimate the approximate particle size to be 80 nm. The contrast is also strong enough to count the particles in the oligomer and to determine their arrangement. While this is less important for the dimer, we can conclude for the quadrumer that it is composed of two pairs of dimers that comprise an angle of their long axis of roughly 80◦ . In the following, we will focus on the analysis of dimers only.

Figure 7: Au-particle based oligomers. (a), (b) threshold PEEM images of a dimer and a quadrumer showing the particles bright as they emit more photoelectrons than the surrounding substrate; (c), (d) MEM images of the same oligomers as in panels (a) and (b), respectively. The particles appear black with a white halo. The particles comprising the oligomers have a diameter of ≈ 80 nm. To investigate the optical polarization sensitivity of the plasmon resonances we use nonlinear photoemission microscopy (nPPE PEEM) 66 . For this experiment, the microscope is combined with a Ti:Sapphire laser system (FEMTOLASERS) delivering femtosecond laser pulses that impinge on the sample surface along the surface normal 67 . The relevant parameters of the laser pulses are their central wavelength of 800 nm (Eph = 1.55 eV), a pulse duration of ≤ 15 fs, and a pulse energy of about 1 nJ. The general optical setup has been described earlier 68,69 . For the work presented here, it is important to emphasize that we can adjust the pulse energy at the sample by using a zero-order

λ/2-waveplate to rotate the polarization direction and combine it with a reection at a glass plate under the Brewster angle. Behind this Brewster reector, we obtain a spolarised beam with adjustable intensity. Using a second zero-order λ/2-waveplate, we can then rotate the linear polarization direction to any orientation within the surface plane. The combination of the Brewster reector with the two waveplates allows us to adjust intensity and polarisation independently. We will now discuss the nPPE results in Fig. 8. Two dierent dimers that were selected 17



and analyzed are shown in the top and bottom of Fig. 8 (b). By design, the dimers were fabricated to exhibit a resonant gap mode 70,71 at 800 nm. The highest electron yield is found in the region of the gap between the particles comprising the dimer 71,72 , reecting the high electrical eld enhancement there 7376 . If the polarization is rotated, the electron yield will vary since the electron emission from the gap is strongly polarization dependent. Fig. 8 (a) analyzes the polarization dependence for the two dimers in panel (b) in 1◦ steps. More specically, the green data points correspond to the dimer in the top of Fig. 8 (b) while the red data points correspond to the dimer in the bottom of that panel. The radial coordinate in Fig. 8 (a) is proportional to the detected electron yield, while the azimuthal coordinate describes the polarization angle on the equator of the Poincaré sphere. The electron emission from the two dimers exhibits distinct maxima at particular polarization angles where the gap mode can be eciently excited. This is the case whenever the polarization is aligned with the long axis of the dimer. Following this argument, we can determine the orientation of the dimers on the surface with high precision. The two dimers that we analyzed are apparently rotated with respect to each other by 21◦ .

Figure 8: Polarization dependence of the emission characteristics. (a) electron emission yield of the two dimers shown in panel (b) as function of polarization angle. The electron emission yield of the two dimers shows a maximum whenever the polarization is aligned to the long axis of the dimer. The solid lines are ts following a 4th order emission process. The green and red solid lines in Fig. 8 (a) are numerical ts through the data

Y (ϑ) ∝ cos2n (ϑ) with Y (ϑ) for the measured electron yield and ϑ for the polariza18


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tion angle. The t parameter n indicates the order of the nonlinear electron emission process. For the case of the two dimers discussed here, we nd values for n ≈ 4, which indicates that 4 quanta from the superposition of the laser's electric eld and the plasmonic resonance are necessary to emit one electron. The particles' surfaces are thus suciently clean to maintain the high work-function of pristine Au of 5.3 eV and all lower nonlinear emission processes are suppressed. Also, in Fig. 8 (a) the maximum electron emission yield from the dimer in panel (b) corresponding to the green data points amounts to only ≈ 70 % of the one from the dimer in panel (c) with red data points. Considering the nonlinear character of the emission process, however, the 30 % lower electron emission translates into a dierence in eld enhancement of only 9 %. Apparently, the eld enhancement characteristics of the two dimers are very similar.

Figure 9: Laser-power dependence of the nonlinear electron emission yield for the two dimers shown in the insets. The order of the emission process can be determined from the slope of the lines in the double-logarithmic plot. Figure 9 shows an analysis of the emission yield of two dierent dimers as function of the overall average laser power. The two dimers are again indicated by red and green data points, and nPPE PEEM images of the dimers are shown as insets. The yield on the ordinate of Fig. 9 corresponds to the integral intensity of a region of interest placed on the dimer. The polarization was adjusted and then xed to achieve roughly comparable emission yields from both dimers. In the double-logarithmic representation, the nonlinear emission is represented by lines following a power law Y (P ) = P n , i.e., from the slope of the lines we can extract the order of the emission process n with great accuracy. For 19



the dimer marked in red, we nd n=4.0, consistent with the analysis in the polar plot Fig. 8. The dimer with the green frame in Fig. 9 shows n = 4.4 which seems surprising as it suggests a fractional number of energy quanta to be absorbed during the emission of each electron. Based on our earlier work on nonlinear plasmoemission 77 , we know that in nonlinear electron emission from plasmons several emission pathways can exist in parallel. If the eld enhancement is high enough, not only a 4th order process, but also a 5th order process will become possible. As our data presented here is not energy ltered, both emission pathways will contribute to the yield, and any contribution from a 5th order (or higher) process will push the measured value for n above n=4. The explanation is consistent with the nding n=4 for the particle with the red frame, as the overall emission yield of that particle is smaller, and the 5th order process will play a lesser role. Linear and nonlinear photoemission microscopy in combination with mirror electron microscopy was used to investigate oligomers composed of self-assembled Au particles. In the microscope we can clearly identify the size of the particles and their arrangement. Most of the oligomers are dimers, and they exhibit substantial electrical eld enhancement due to the plasmonic mode formed in the gap between the particles. In nonlinear photoemission microscopy we can visualize that the strongest eld is indeed localized in the gap, and the nonlinear character of the 4th order electron emission mechanism is indication of substantial eld enhancement at this position. We observe the expected polarization dependence, i.e., the gap mode is excited when the light's polarization vector is aligned with the long axis of the dimer. By rotating the polarization direction and by comparing the maximal photoemission yield from two dierent dimers we nd that the electric elds in the gap of the two dimers only dier by about 9%. Based on this analysis we conclude that the self assembly method used to produce the dimers yields a very dened and reproducible gap.

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Outlook Chemists are nowadays able to synthesize highly spherical gold nanoparticles and to assemble them into well-dened structures such as dimers with well-dened short gaps and distance control at the Angström level. This uniformity and reproducibility across a set of single colloidal particles (monomers and dimers) is expressed by the term precision plasmonics. Optical spectroscopy, however, is generally limited in terms of both its structural information content (as it typically probes the electronic system and not the lattice) and its spatial resolution (diraction limit). These drawbacks can be overcome by using electrons to interrogate plasmonic systems at the time and space limit. By directly probing the non-equilibrium lattice dynamics by femtosecond electron diraction after ultrafast optical excitation, researchers are nowadays able to monitor the evolution of stress and heat in plasmonic nanostructures in the time domain. This provides fundamentals insight into the coupling between the electronic system and the metal lattice in the spatially conned dimensions of a noble metal nanoparticle which is physically dierent from the situation in an extended metal lm. The extremely high electric elds generated upon ultrafast optical excitation can induce the ecient generation of hot carriers such as hot electrons which in turn can be extracted to adjacent electron acceptors (semi-conductors, molecules) for solar to chemical energy conversion. Probing these enhanced local electric elds by femtosecond nonlinear photo-emission electron microscopy (PEEM) at the nanoscale provides unique insights into the electronic response of the system after ultrafast optical excitation. Beyond the impact of these techniques on purely metallic nanostructures, one can also easily envision numerous fundamental studies in molecular precision plasmonics where metal/molecule interfaces are present in hybrid structures. Exploiting, for example, the highly uniform gap and in particular the extreme eld enhancement in the gap in SERS will pave the way towards precision SERS where molecules located in the gap of an ideal dimers will ideally shows highly comparable SERS intensities from single dimer to single dimer. Overall, these initial results on monomers and dimers of spherical gold nanoparticles presented in this feature article are highly encouraging as they demonstrate the feasibility of precision plasmonics of single 21



ideal colloidal particles at the limits of time and space after ultrafast optical excitation.

Acknowledgment This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Projektnummer 278162697 - SFB 1242 non-equilibrium dynamics of condensed matter in the time domain (A04, B06, C01). The UED work was performed at SLAC MeV-UED, which is supported in part by the DOE BES SUF Division Accelerator & Detector R&D program, the LCLS Facility, and SLAC under contract Nos. (DE-AC02-05-CH11231) and (DE-AC02-76SF00515). Also nancial support from the German Research Foundation (DFG; INST-20876/2018-1 FUGG) is highly acknowledged.

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Frank Meyer zu Heringdorf is a professor at the University of Duisburg-Essen and member of the Centre for Nano Inegration Duisburg-Essen (CENIDE). He received his Ph. D. in physics with honors from the University of Hannover (Germany) in 1999 and then joined IBM's research center in Yorktown Heights as a postdoctoral Feodor-Lynen Fellow. He then established time-resolved photoemission microscopy as a new method at the University of Essen and obtained his habilitation there in 2010 for a thesis on his microscopy work. He was awarded the Gottschalk-Diederich-Baedeker prize in 2011. Frank's research interests still include low-energy electron microscopy and time-resolved photoemission microscopy with an emphasis on nanoscience and surface plasmons.

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Klaus Sokolowsi-Tinten is a Senior Sta Scientist and Adjunct Professor at the Faculty of Physics of the Universität Duisburg-Essen and a member CENIDE (Center for Nanointegration Duisburg-Essen). He obtained his Diploma and Ph. D. in Physics at the Universität Gesamthochschule Essen. His main research interests are in the eld of ultrafast laser-material interactions with particular emphasis on the investigation of the structural dynamics under strongly non-equilibrium conditions using advanced timeresolved scattering techniques with femtosecond X-ray and electron pulses.

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Sebastian Schlücker is Professor of Physical Chemistry at the University DuisburgEssen and member of the Center for Nanointegration Duisburg-Essen (CENIDE). He received his diploma and Dr. rer. nat. (PhD) in chemistry from the University of Würzburg in 2002 and postdoctoral training at NIH in Bethesda/MD. His research interests are the physics and chemistry of molecularly functionalized plasmonic nanostructures and their application in biomedicine and energy conversion. In 2018 he founded NanoWerke GmbH.

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Precision Plasmonics with Monomers and Dimers of Spherical Gold

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